We remark that the appearance of the reverse time orientation \(\Psi ^*_\mathcal {A}\)  in Def. REF  is a consequence of the identification of bipartite quantum states and quantum channels via Choi's theorem [1]} (for more details, see [2]}). Def. REF  is the missing piece of physical data to identify bipartite non-signalling distributions with quantum states [3]}. Together, this shows that quantum states encode information about the relative time orientation between subsystems.
